A sharp bound for the Stein-Wainger oscillatory integral期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A sharp bound for the Stein-Wainger oscillatory integral

Authors:	Ioannis R. Parissis

Affiliation:	Department of Mathematics, University of Crete, Knossos Avenue, 71409 Iraklio, Crete, Greece

Abstract:	Let $mathcal{P}_d$ denote the space of all real polynomials of degree at most . It is an old result of Stein and Wainger that $displaystyle sup_ {Pinmathcal{P}_d} biggvert p.v.int_{mathbb{R}} {e^{iP(t)}frac{dt}{t}} biggvertleq C_d$ for some constant depending only on . On the other hand, Carbery, Wainger and Wright claim that the true order of magnitude of the above principal value integral is . We prove that $displaystyle sup_ {Pinmathcal{P}_d}biggvert p.v. int_{mathbb{R}}{e^{iP(t)}frac{dt}{t}}biggvertsim log{d}.$

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